Title: Direct computation of period doubling bifurcation points of large-scale systems of ODEs using a Newton-Picard method
Authors: Engelborghs, Koen ×
Lust, Kurt
Roose, Dirk #
Issue Date: Oct-1999
Publisher: Academic Press
Series Title: IMA Journal of Numerical Analysis vol:19 issue:4 pages:525-547
Abstract: Periodic solutions of certain large-scale systems of ODEs can be computed efficiently using a hybrid Newton-Picard scheme, especially in a continuation context. In this paper we describe and analyse how this approach can be extended to the direct computation of period doubling bifurcation points. The Newton-Picard scheme is based on shooting and a splitting of the state space in a low-dimensional subspace corresponding to the weakly stable and unstable modes and its orthogonal complement. The method avoids the computation of the full monodromy matrix, which is present in the determining system for period doubling bifurcation points. Test results are presented that demonstrate the numerical properties.
ISSN: 0272-4979
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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